Earlier this month, in Lecture Theatre 2 in the Andrew Wiles Building, a collection of talented Oxford Mathematics students, together with colleagues in STEM subjects and beyond, performed Fermat's Last Tango to sell-out crowds over five performances.
Written in 2000 by Joanne Sydney Lessner and Joshua Rosenblum, Fermat's Last Tango tells the story, in words and music, of a 300 hundred-year-old mathematical mystery and the man who spent seven years trying to solve it. Sound familiar?
A complex irreducible admissible representation of a reductive p-adic group is typically infinite-dimensional. To quantify the "size" of such representations, we introduce the concept of canonical dimension. To do so we have to discuss the Moy-Prasad filtrations. These are natural filtrations of the parahoric subgroups. Next, we relate the canonical dimension to the Harish-Chandra local character expansion, which expresses the distribution character of an irreducible representation in terms of nilpotent orbital integrals. Using this, we consider the wavefront set of a representation. This is an invariant the naturally arises from the local character expansion. We conclude by explaining why the canonical dimension might be considered a weaker but more computable alternative to the wavefront set.
Fermat's Last Tango, written in 2000 by Joanne Sydney Lessner and Joshua Rosenblum, tells the story, in words and music, of a 300 hundred-year-old mathematical mystery and the man who spent seven years trying to solve it.
This version was performed in early March 2023 by Oxford Mathematics students and fellow students from across the University. The venue was a lecture theatre in the Andrew Wiles Building, home to Oxford Mathematics and named after the mathematician who is the subject of the story.
